Percolation Point Research Articles

Chitosan-based hydrogels: Influence of crosslinking strategy on rheological properties

The effect of two crosslink strategies on the preparation of chitosan-based covalent hydrogels was investigated employing the widely used thiol-ene reaction. This versatile “click” chemistry can be activated either photochemically or thermochemically. Initially, well-purified chitosan (CS, DA ∼4 %, Mw ∼580 kg mol−1) was separately functionalized with vinyl (CS-ene) or thiol (CS-SH) groups in aqueous media. Subsequently, two strategies were compared where thiol-ene reaction occurs respectively between: (S1) modified chitosans CS-ene and CS-SH, in a polymer – polymer strategy, and (S2) CS-ene and di(ethylene glycol) dithiol (dEG-(SH)2), in a polymer – molecule strategy.Both crosslinking strategies were evaluated through rheological measurements, starting with entangled chitosan solutions. The difference in diffusion of functional groups, whether attached to polymer chains or to free molecules, leads to faster gelation kinetics with S2. Consequently, stronger gels were obtained with S2, where the modulus was connected with the degree of functionalization, while S1 produced weaker gels closer to the percolation point, where crosslinked density was associated with the entanglement number derived from the initial concentration. Nevertheless, networks formed by both strategies were homogenous with minimal dissipative contributions to their rheological properties, indicating that structural defects are negligible.

Attractive carbon black dispersions: Structural and mechanical responses to shear

The rheological behavior of colloidal dispersions is of paramount importance in a wide range of applications, including construction materials, energy storage systems, and food industry products. These dispersions consistently exhibit non-Newtonian behaviors, a consequence of intricate interplays involving colloids morphology, volume fraction, and interparticle forces. Understanding how colloids structure under flow remains a challenge, particularly in the presence of attractive forces leading to cluster formation. In this study, we adopt a synergistic approach, combining rheology with ultra small-angle x-ray scattering, to probe the flow-induced structural transformations of attractive carbon black (CB) dispersions and their effects on the viscosity. Our key findings can be summarized as follows. First, testing different CB volume fractions, in the high shear rate hydrodynamic regime, CB particles aggregate to form fractal clusters. Their size conforms to a power law of the shear rate, ξc∝γ˙−m, with m≃0.5. Second, drawing insights from the fractal structure of clusters, we compute an effective volume fraction ϕeff and find that microstructural models adeptly account for the hydrodynamic stress contributions. We identify a critical shear rate γ∗˙ and a critical volume fraction ϕeff∗, at which the clusters percolate to form a dynamical network. Third, we show that the apparent yield stress measured at low shear rates inherits its properties from the percolation point. Finally, through data scaling and the integration of Einstein’s viscosity equation, we revisit and discuss the Caggioni–Trappe–Spicer model, revealing a significant connection between its empirical parameters and the structural properties of CB dispersions under flow.

The Influence of the Phase Arrangement of ATZ Composites on Their Wear Rate Under Ball-on-Disc Tests

An alumina-toughened zirconia (ATZ) material, fabricated using a procedure consisting of the common sintering of two different zirconia powders, was tested using the ball-on-disc method in a temperature range between 20 and 400 °C. Tetragonal zirconia balls were used as a counterpart. Three different types of microstructure were designed, one consisting in separated alumina inclusions in zirconia matrix, the second one containing alumina inclusion in the amount close to the percolation point and another one which was a combination of two continuous phases, penetrating the whole volume of the composite. It was detected that at elevated temperatures all materials showed distinct decrease of measured wear rate. Composite with a low alumina content showed minimal wear rate at 300 °C and composites with higher amount of alumina were the most wear resistant at 400 °C. There are some evidences that this minimal wear rate is connected with a pseudoplastic behavior of a layer formed between co operating elements of tribological pair.

Networks of Limited-Valency Patchy Particles.

Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.

Virtual lesions in MEG reveal increasing vulnerability of the language network from early childhood through adolescence

In childhood, language outcomes following brain injury are inversely related to age. Neuroimaging findings suggest that extensive representation and/or topological redundancy may confer the pediatric advantage. Here, we assess whole brain and language network resilience using in silico attacks, for 85 children participating in a magnetoencephalography (MEG) study. Nodes are targeted based on eigenvector centrality, betweenness centrality, or at random. The size of each connected component is assessed after iterated node removal; the percolation point, or moment of dis-integration, is defined as the first instance where the second largest component peaks in size. To overcome known effects of fixed thresholding on subsequent graph and resilience analyses, we study percolation across all possible network densities, within a Functional Data Analysis (FDA) framework. We observe age-related increases in vulnerability for random and betweenness centrality-based attacks for whole-brain and stories networks (adjusted-p < 0.05). Here we show that changes in topology underlie increasing language network vulnerability in development.

Rheological percolation, gel‐like behavior and electrical conductivity of multi‐walled carbon nanotubes filled ethylene‐vinyl acetate copolymer/acrylonitrile‐butadiene rubber nanocomposites

AbstractReasonable studies on the composite systems containing conductive nanoparticles are very important to manufacture the materials with physico‐mechanical tailor‐made properties. In this work, rheological percolation, gel‐like behavior and electrical properties of multi‐walled carbon nanotubes (MWCNTs) filled ethylene‐co‐vinyl acetate/acrylonitrile‐butadiene copolymer blends containing 0–7 wt% MWCNTs were studied. The Winter‐Chambon criterion validity was evaluated for physical gelation of the system. The rheological and electrical percolation threshold, gel point (Pg), relaxation exponent (n), gel strength (Sg), and the fractal dimension (df) at the gel point were calculated. The formation of physical gel and rheological percolation threshold were both found to occur at 1 wt% MWCNTs concentration. Based on the df value determined, it was revealed that the system behaved similar to the one in which the excluded volume interactions were nearly screened. It was also found that the storage modulus (G′) near the Pg followed a power‐law scaling relationship in the form where is the distance from Pg. The electrical conductivity of the nanocomposites increased with the increase in MWCNTs loading after the nanofillers content surpassed a certain value. A schematic model was proposed to demonstrate the variation of electrical conduction with the increase in MWCNTs concentration. The excluded volume and hard‐core models were also employed to estimate the average aspect ratio of the nanofillers embedded in the system.Highlights Morphology and gel‐like behavior of EVA/NBR/MWCNTs system were studied Winter‐Chambon criterion was found to be valid for the gelation of the system Rheological percolation and gel point were occurred at the same MWCNTs loading It was found excluded volume interactions were nearly screened at gel point A schematic model for microstructure development was suggested for the system

Modelling network formation in folded protein hydrogels by cluster aggregation kinetics.

Globular folded protein-based hydrogels are becoming increasingly attractive due to their specific biological functionality, as well as their responsiveness to stimuli. By modelling folded proteins as colloids, there are rich opportunities to explore network formation mechanisms in protein hydrogels that negate the need for computationally expensive simulations which capture the full complexity of proteins. Here we present a kinetic lattice-based model which simulates the formation of irreversibly chemically crosslinked, folded protein-based hydrogels. We identify the critical point of gel percolation, explore the range of network regimes covering diffusion-limited to reaction-limited cluster aggregation (DLCA and RLCA, respectively) network formation mechanisms and predict the final network structure, fractal dimensions and final gel porosity. We reveal a crossover between DLCA and RLCA mechanisms as a function of protein volume fraction and show how the final network structure is governed by the structure at the percolation point, regardless of the broad variation of non-percolating cluster masses observed across all systems. An analysis of the pore size distribution in the final network structures reveals that, approaching RLCA, gels have larger maximal pores than the DLCA counterparts for both volume fractions studied. This general kinetic model and the analysis tools generate predictions of network structure and concurrent porosity over a broad range of experimentally controllable parameters that are consistent with current expectations and understanding of experimental results.

Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model.

After a sudden quench from the disordered high-temperature T_{0}→∞ phase to a final temperature well below the critical point T_{F}≪T_{c}, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time t_{p_{1}}>0) and stabilization (at time t_{p}>t_{p_{1}}) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (T_{F}=0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t,p) and the typical domain size ℓ(t,p) have no dependence on p in the first time regime up to t_{p_{1}}. Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at t_{p_{1}} is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: t_{p}(p)∼p^{-1} for p≪1 (at p=0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, t_{p_{1}} and t_{p} in such systems.

Research on novel battery thermal management system coupling with shape memory PCM and molecular dynamics analysis

• A novel SCPCM with shape memory and shape stability is proposed. • The interaction of PA/SEBS was analyzed at the molecular level. • SCPCM shows good thermal stability at a temperature range higher than PA phase transition. • Under discharge conditions of 3C, the temperature difference in the PCM module is kept within 3℃. Traditional battery thermal management using phase change materials (PCM) is restricted by PCM’s leakage, low thermal conductivity and incompatibility. In this work, a shape memory composite PCM (SCPCM) composed of styrene-b-(ethylene-co-butylene)-b-styrene triblock copolymer (SEBS), paraffin (PA), expanded graphite (EG) and Fe 3 O 4 -modified graphene oxide (Fe 3 O 4 -MGO) was prepared. The thermal properties and shape stability of the composite material were studied. The compatibility between the phase change matrix and the support material was investigated. The results show that reducing the size of EG particles can effectively reduce the thermal conduction “percolation point”. The Fe 3 O 4 -MGO particles loaded on EG can effectively reduce the interfacial thermal resistance between EG and PA then further strengthen the heat transfer capability of CPCM. SCPCM shows good thermal stability in the range of phase transition temperature higher than PA (49–85 °C). The simulation results show that PA and SEBS molecules exhibit good interfacial compatibility, hydrogen bonds are formed between the molecules where there is a strong interaction. Therefore, PA/SEBS show good thermal stability in the macro system. SCPCM exhibits excellent performance in heat dissipation. Under discharge conditions of 3C, the temperature difference in the SCPCM module is kept within 3 °C.

Nonvanishing optimal noise in cellular automaton model of self-propelled particles

A minimal cellular automaton model is introduced to describe the collective motion of self-propelled particles on two-dimensional square lattice. The model features discretization of directional and positional spaces and single-particle occupation on one lattice site. Contrary to the Vicsek model and its variants, our model exhibits the nonvanishing optimal noise. When the particle density increases, the collective motion is promoted with optimal noise strength and reduced with noise strength out of optimal region. In addition, when the square lattice undergoes edge percolation process, no abrupt change of alignment behaviors is observed at the critical point of percolation.

Hierarchical Porous Magnetite Structures: From Nanoparticle Assembly to Monolithic Aerogels

The development of universal methods to synthesize materials with different structures is always in the researchers’ focus. Despite the fact that various structures based on magnetite have already been obtained, synthetic approaches that allow to synthesize materials with a wide range of texture and functional properties are still very poorly presented. In this work, we demonstrate that a stable magnetite hydrosol can be easily converted into monolithic structures of xero-, cryo- and aerogel by careful varying concentrations and drying conditions. We have also theoretically explained the observed effects by studying the percolation threshold at the sol–gel transition by means of controlled assembly of magnetite nanoparticles. At the calculated percolation point three types of materials different in porous organization were obtained. Due to the high biocompatibility of magnetite nanoparticles, the materials obtained were evaluated for cytotoxicity on HeLa cells line. All synthesized magnetite structures show excellent biocompatibility and minor cytotoxic effects at concentrations up to 1 µg mL−1. Considering that the porosity of materials can influence the manifestation of the hemostatic effect, whole-blood clotting study revealed the hemostatic potential of magnetite aerogel. That fact can be explained by presence spongy structure of the aerogel that allowed blood to be rapidly absorbed through full contact.

Expansion for the critical point of site percolation: the first three terms

AbstractWe expand the critical point for site percolation on the d-dimensional hypercubic lattice in terms of inverse powers of 2d, and we obtain the first three terms rigorously. This is achieved using the lace expansion.

Percolation transitions in pyrochlore: Radiation-damage and thermally induced structural reorganization

Finite element mechanical modeling is used to follow the evolution of the hardness (H), Young's modulus (E), and Poisson's ratio (ν) during the radiation-damage related crystalline-to-amorphous transition in pyrochlore (average main composition Ca2Nb2O6F). According to the model, two percolation transitions have been identified around 16% and 84% amorphous volume fraction, respectively. In this context, earlier results from thermally induced recrystallization experiments have found to indicate noticeable modifications on the short- and long-range order by passing the percolation thresholds. Both percolation points have found to act as specific kinetic barriers during stepwise annealing induced structural reorganization. As phases with pyrochlore structure have been considered as host structures for the long-term disposal of actinides, it is essential to gain better knowledge of their mechanical behavior under radiation-damage and subsequent temperature treatment. The obtained results validate the used models' robustness in predicting radiation-damage related mechanical modifications, at least for ceramics.

In situ monitoring of electrical resistivity and plasma during pulsed laser deposition growth of ultra-thin silver films

Ultra-thin silver films of thicknesses of the order of 10 nm and less were prepared in different ambient conditions (vacuum, Ar, and N2) by pulsed laser deposition on glass and fused silica substrates. The in situ monitoring of electrical resistance of deposited films and optical emission spectroscopy of plasma were implemented as real-time analysis techniques. Change in the growth mechanism of the Ag layer in N2 ambient is expressed by an acceleration of the coalescence process, which shifts the percolation point toward lower mass thicknesses. The films prepared in vacuum and Ar ambient were found to be unstable for a final resistance in the range from 1 to 100 MΩ while the films deposited in N2 revealed stable electrical resistance. The percolation point was further lowered by introducing a sublayer of AgxOy for the film deposited in N2 gas. Based on data provided by AFM, SEM, and spectroscopic ellipsometry, different film formation mechanisms are discussed in relation to surface morphology and optical properties. Optical emission spectroscopy was used to monitor the deposition process and identify the species presented during the deposition process. The energy of the ejected particle is affected by the addition of ambient gas and depends on the properties of the working gas.

Synergistic Effect of MWCNT and Carbon Fiber Hybrid Fillers on Electrical and Mechanical Properties of Alkali-Activated Slag Composites

Herein, we investigated the synergistic effect of multi-walled carbon nanotube (MWCNT) and carbon fiber (CF) hybrid fillers on electrical and mechanical characteristics of alkali-activated slag (AAS) composites. Many studies on AAS composites have been conducted in the past; however, not much progress has been made regarding characteristics of AAS composites with hybrid conductive fillers. The specimens with different mix proportions were fabricated in the present study, and numerous material characteristics, including flowability, electrical resistivity, and compressive strength of AAS composites were measured. In addition, the synergistic effects were investigated through scanning electron microscopy and thermogravimetric analysis. It was found that the 0.5 wt.% of MWCNTs and CFs lead the effects of the bridging and reducing crack propagation, thereby improving its electrical and mechanical performances. The filler exceeding a percolation point improved the electrical performance of the AAS composites; however, it interfered with the hydration process during the curing period, and caused a decrease in compressive strength of AAS composites.

Effect of Wood Fiber Loading on the Chemical and Thermo-Rheological Properties of Unrecycled and Recycled Wood-Polymer Composites

Novel wood fiber (WF)-polypropylene composites were developed using the extrusion process with a twin-screw extruder. The influence of different mass addition of WF to unrecycled polypropylene (PP) and recycled PP (R-PP) on the chemical, thermal and rheological properties of the processed WF-PP and WF-R-PP composites was investigated. For this purpose, the chemical surface structure of the composites was followed with ATR-FTIR (attenuated total reflection Fourier transform infra red spectroscopy), while the thermal properties of the WF-PP composites were investigated with differential scanning calorimetry (DSC). Furthermore, the crystalline structure of the composites was determined by X-ray diffraction (XRD) analysis. Finally, the rheology of the materials was also studied. It was observed that a stronger particle formation at high additional concentrations was observed in the case of recycled PP material. The addition of WF over 20% by weight increased the crystallinity as a result of the incorporation and reorganization of the WF and also their reinforcing effect. The addition of WF to pure PP had an influence on the crystallization process, which due to the new β phase and γ phase PP formation showed an increased degree of crystallinity of the composites and led to a polymorphic structure of the composites WF-PP. From the rheological test, we can conclude that the addition of WF changed the rheological behavior of the material, as WF hindered the movement of the polymeric material. At lower concentrations, the change was less pronounced, although we observed more drastic changes in the material behavior at concentrations high enough that WF could form a 3D network (percolation point about 20%).

Existence of phase transition for percolation using the Gaussian free field

In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension $d>4$ undergoes a non-trivial phase transition (in the sense that $p_c<1$). As a corollary, we obtain that the critical point of Bernoulli percolation on infinite quasi-transitive graphs (in particular, Cayley graphs) with super-linear growth is strictly smaller than 1, thus answering a conjecture of Benjamini and Schramm. The proof relies on a new technique consisting in expressing certain functionals of the Gaussian Free Field (GFF) in terms of connectivity probabilities for percolation model in a random environment. Then, we integrate out the randomness in the edge-parameters using a multi-scale decomposition of the GFF. We believe that a similar strategy could lead to proofs of the existence of a phase transition for various other models.

Topological effects and conformal invariance in long-range correlated random surfaces

We consider discrete random fractal surfaces with negative Hurst exponent H&lt;0H&lt;0. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level hh. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter (HH) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value h=h_ch=hc and for H\leq-\frac{3}{4}H≤−34 the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For -\frac{3}{4}&lt;H&lt; 0−34&lt;H&lt;0 instead, there is a line of critical points with continously varying exponents. The universality class of these points, in particular concerning the conformal invariance of the level clusters, is poorly understood. By combining the Conformal Field Theory and the numerical approach, we provide new insights on these phases. We focus on the connectivity function, defined as the probability that two sites belong to the same level cluster. In our simulations, the surfaces are defined on a lattice torus of size M\times NM×N. We show that the topological effects on the connectivity function make manifest the conformal invariance for all the critical line H&lt;0H&lt;0. In particular, exploiting the anisotropy of the rectangular torus (M\neq NM≠N), we directly test the presence of the two components of the traceless stress-energy tensor. Moreover, we probe the spectrum and the structure constants of the underlying Conformal Field Theory. Finally, we observed that the corrections to the scaling clearly point out a breaking of integrability moving from the pure percolation point to the long-range correlated one.

Relating chemical composition, structure, and rheology in alkali‐activated aluminosilicate gels

AbstractModel aluminosilicate (N‐A‐S‐H) gel systems give insight to the complex reaction occurring in alkali‐activated binders, allowing for more precise control over chemical composition and exhibiting simpler kinetics. Small angle neutron scattering, oscillatory rheology, and solid‐state NMR were used to characterize N‐A‐S‐H gel samples and relate structure, chemical composition, and rheology. Aluminum concentration was varied in the gel samples at fixed silica and sodium concentration. Past the percolation point, the gel develops in two regimes distinct in structure and rheological behavior. The first gel regime is characterized by increase in modulus and initial formation of fractal structures following a diffusion‐limited monomer‐cluster aggregation mechanism. The second gel regime at higher aluminum concentrations is characterized by a modulus plateau and structure development via reaction‐limited aggregation of existing clusters. NMR data indicate a saturation of aluminum in the network at the transition between gel regimes, which may be pH driven. Understanding the structure‐property relationships critical to formation of the N‐A‐S‐H gel can give valuable insight to the reaction mechanism in alkali‐activated binders and the influence of chemical composition on resultant structure and mechanical properties.

(Invited) Percolation Carbon Nanotube Thin Film Transistors

The decrease of the gate voltage swing switching a field effect transistor from on to off state and, consequently, the decrease of the power supply voltage is the key challenge of the transistor design. Gate voltage dependent tunneling has been used to achieve this goal by decreasing the slope of the exponential current decay in the subthreshold regime below 60 mV per decade. We describe a new Carbon Nanotube (CNT) Percolating Thin Film Transistor (PTFT) that should allow achieving a steep subthreshold slope. CNT TFTs use mats of CNTs deposited on a substrate and forming a random percolating network. The conduction contacts between the individual CNTs is determined by tunneling and, therefore, could be strongly affected by external agents, such as gases or biological fluids. The asymmetry of the contacts to each CNT enables the rectification of electromagnetic radiation impacted on the CNT mat changing the drain-to-source conduction, with giant relative changes near the percolation point. Our experimental data show that sub-THz radiation shifts the percolation point at high intensity, when the rectified radiation changes the shape of the potential barrier between the CNT in a proximity contact. The CNT PTFT operates near the percolation point. In this regime, the gate bias shifts the percolation point by (a) depleting the CNTs in the subthreshold regime and (b) changing the shape of the tunneling barrier. This ensures the metal-insulator transition resulting in a sharp decrease of the subthreshold current slope. We present a compact model of the percolated CNT PTFT based on our Unified SPICE/ADS model that shows that this effect could reduce the subthreshold slope of the CNT TFs from 340 meV per decade to about 190 meV per decade.AcknowledgmentsThis work at RPI was supported by the U.S. Army Research Laboratory under the Cooperative Research Agreement (Project Monitor Dr. Meredith Reed) and by the US ONR (Project Monitor Dr. Paul Maki).